Q.

If A=cos⁡α−sin⁡α0sin⁡αcos⁡α0001, then (Adj⁡A)−1=

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a

cosα−sinα0sinαcosα0001

b

−cosα−sinα0sinα−cosα0001

c

−cosαsinα0sinα−cosα0001

d

1000cosα−sinα0sinαcosα

answer is A.

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Detailed Solution

det  A=cosαcosα−0+sinαsinα−0=cos2α+sin2α=1∴A−1=Adj  A⇒Adj  A−1=A−1−1=A
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If A=cos⁡α−sin⁡α0sin⁡αcos⁡α0001, then (Adj⁡A)−1=